Shom Code

Each alphabet letter is assigned a code made only of 0s and 1s. A code may also have length 0. To encode a string, replace its letters from left to right by their assigned codes and concatenate the results.

For instance, suppose the alphabet set is {a, b, c, d} and the assignment is f(a)=1, f(b)=1010, f(c)=01, and f(d)=10101. Then the string cac is encoded as 01101 by concatenating 01, 1, and 01.

If one binary code can be interpreted as two different strings, it is ambiguous. If it can be interpreted as three or more different strings, it is really ambiguous. Under the assignment above, 10101 is really ambiguous because it can be interpreted as ba, acc, and d.

Given the list of assigned codes, find the minimum length of a binary code that can be interpreted as three or more different strings.

The first line contains the number of codes N. N is an integer between 2 and 26, inclusive.

Each of the next N lines contains the code assigned to one alphabet letter. Each code consists only of 0s and 1s and has length at most 50. A code of length 0 is given as -1. Different letters may have identical codes.

Print the minimum length of a binary code that can be interpreted as three or more different strings. If no such code exists, print -1.